# 英国留学生带你回忆被数学支配的恐惧

Key Points:

Einstein用 Riemann Geometry 数学救了Newton 物理。

3位大师救近代中国数学: 华罗庚, 陈省身, 苏步青

[纠正]: Andrew Wiles 超过40岁, 没赶上Fields Medal, 只得个”奖励”。他看到椭圆(Ellipse)气球, 得到突破 FLT “工具”的灵感 – “Elliptic Curve” 。

# Six books that have shaped my mathematical worldview

First book: The 17th CE French Mathematician-cum-Judge Fermat is the name of my alma-mater French Engineering (undergraduate) University.

A self-study Russian mathematician, kicked out 3 times in high schools, expelled from Moscow University, all because he did not attend classes, preferred to self-study in a broader scope for his curiosity, at his own faster speed than the rigid curriculum and boring test-and-exams regime in classrooms.

He did the PhD in Harvard by invitation even he did not have a Bachelor degree, and he barely passed the Harvard’s QE (Qualifying Exams) in Algebraic Geometry, a field in which he made a revolutionary discovery few years later, and for which he was awarded the highest honor : Fields Medal.

This is the typical trait of the geniuses like Evariste Galois, Albert Einstein, Ramanujian, Hua Luogeng (华罗庚), Zhang YiTang (张益唐 – proved “70m Twin Prime Gap”) [#] , Chen Jingrun (陈景润, proved Goldbach Conjecture “1+2”) [##]… with self-motivated curiosity in their field of passion, with reading from the Masters’ works by themselves, PLUS thinking on a problem over many years with perseverance, they finally made great discoveries !

Keywords:

1. Topology 拓扑
2. Algebraic Geometry 代数几何: Geometry and Algebraic Equations
3. Motif: Grothendieck
4. Homotopy Theory 同伦

Notes:

# How (not) to memorise mathematics

Many excellent Math students after leaving universities more than 10 years forget 90% of math they learned, save some primary school arithmetics – few could do Singapore PSLE Modelling Math or solve quadratic equations.

The “Story-Telling” memory technique via “Signposts” can be used to reconstruct math from first principles:

https://medium.com/@fjmubeen/how-not-to-memorise-mathematics-98fef71aefcf

Note: Lewis Carroll: the author of “Alice in wonderland”

Cambridge Professor Tim Gowers (Fields Medalist) suggested the similar pedagogy of “Memorise by First Principles”.

# What is math?

What is Math ? Interesting article below:

https://infinityplusonemath.wordpress.com/2017/06/17/what-is-math/

• Mathematics = “that which is learned“ –(Pythagoras)

Math is not about calculation, it is understanding the nature, the universe, the philosophy (logic, intelligence – both “human” and “artificial”)…

What is Axiom, Lemma, Proposition ? Why rigorous Calculus was needed hundred years after Newton & Leibniz had invented it – “Epsilon-Delta” Analysis.

Difference between Riemann Integral & Lebesgue Integral ?

# Unknown German Retiree Proved The “Gaussian Correlation Inequality” Conjecture

https://www.wired.com/2017/04/elusive-math-proof-found-almost-lost

$\boxed {P (a + b) \geq P (a) \times P (b)}$

Case “=” : if (a, b) independent
Case “>” : if (a, b) dependent

Thomas Royen used only high-school math (function, derivative) in his proof in 2014. He then published it in arxiv.org website – like Perelman did with the “Poincaré Conjecture”.